Editing Fibonacci (section)

==''Liber Abaci''==
{{Main|Liber Abaci}}
[[Image:Liber abbaci magliab f124r.jpg|thumb|A page of Fibonacci's {{Lang|la|[[Liber Abaci]]}} from the [[National Central Library (Florence)|Biblioteca Nazionale di Firenze]] showing (in box on right) the Fibonacci sequence with the position in the sequence labeled with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals]]
In the {{Lang|la|Liber Abaci}} (1202), Fibonacci introduced the so-called ''modus Indorum'' (method of the [[India]]ns), today known as the [[Hindu–Arabic numeral system]],<ref name="Sigler2002">{{citation | title = Fibonacci's Liber Abaci | translator-last = Sigler | translator-first = Laurence E.  | publisher = Springer-Verlag | year = 2002 | isbn = 0-387-95419-8}}</ref><ref>Grimm 1973</ref> with ten digits including a [[zero]] and [[positional notation]]. The book showed the practical use and value of this by applying the numerals to commercial [[bookkeeping]], converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. Replacing Roman numerals, its [[ancient Egyptian multiplication]] method, and using an [[abacus]] for calculations, was an advance in making business calculations easier and faster, which assisted the growth of [[banking]] and [[accounting]] in Europe.<ref name="Fibonacci: The Man Behind The Math">{{Cite web|title = Fibonacci: The Man Behind The Math|url = https://www.npr.org/2011/07/16/137845241/fibonaccis-numbers-the-man-behind-the-math|website = NPR.org|access-date = 2015-08-29|archive-date = 2011-07-16|archive-url = https://web.archive.org/web/20110716211651/https://www.npr.org/2011/07/16/137845241/fibonaccis-numbers-the-man-behind-the-math|url-status = live}}</ref><ref name="DevlinKeith">{{Cite web|title = The Man of Numbers: Fibonacci's Arithmetic Revolution [Excerpt]|url = http://www.scientificamerican.com/article/the-man-of-numbers-fibona/|access-date = 2015-08-29|first = Keith|last = Devlin|website = [[Scientific American]]|archive-date = 2014-06-18|archive-url = https://web.archive.org/web/20140618102122/http://www.scientificamerican.com/article/the-man-of-numbers-fibona/|url-status = live}}</ref>

The original 1202 manuscript is not known to exist.<ref name="JSG" /> In a 1228 copy of the manuscript, the first section introduces the numeral system and compares it with others, such as [[Roman numerals]], and methods to convert numbers to it. The second section explains uses in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses [[irrational numbers]] and [[prime numbers]].<ref name="JSG">{{Cite web|title = The Man Behind Modern Math|url = http://www.barrons.com/articles/the-man-behind-modern-math-1440227497|access-date = 2015-08-28|first = John Steele|last = Gordon|author-link = John Steele Gordon|archive-date = 2015-08-23|archive-url = https://web.archive.org/web/20150823132758/http://www.barrons.com/articles/the-man-behind-modern-math-1440227497|url-status = live}}</ref><ref name="Fibonacci: The Man Behind The Math"/><ref name="DevlinKeith" />